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From: Richard Damon <richard@damon-family.org>
Newsgroups: comp.theory
Subject: Re: Unpartial Halt Deciders --- category error 2
Date: Sat, 19 Apr 2025 19:15:09 -0400
Organization: i2pn2 (i2pn.org)
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On 4/19/25 4:58 PM, olcott wrote:
> On 4/19/2025 3:27 PM, Keith Thompson wrote:
>> Mr Flibble <flibble@red-dwarf.jmc.corp> writes:
>>> On Sat, 19 Apr 2025 13:34:40 -0400, Richard Damon wrote:
>>>> On 4/19/25 8:05 AM, Mr Flibble wrote:
>>>>> On Sat, 19 Apr 2025 07:55:55 -0400, Richard Damon wrote:
>> [...]
>>>>>>> On 4/18/2025 2:32 PM, Keith Thompson wrote:
>>>>>>>> Mr Flibble <flibble@red-dwarf.jmc.corp> writes:
>>>>>>>>> On Fri, 18 Apr 2025 12:25:36 -0700, Keith Thompson wrote:
>>>>>>>>>> Mr Flibble <flibble@red-dwarf.jmc.corp> writes:
>>>>>>>>>>> I, aka Mr Flibble, have created a new computer science term, the
>>>>>>>>>>> "Unpartial Halt Decider".  It is a Halt Decider over the domain
>>>>>>>>>>> of all program-input pairs excluding pathological input (a
>>>>>>>>>>> manifestation of the self referencial category error).
>>>>>>>>>> [...]
>>>>>>>>>>
>>>>>>>>>> Do you have a rigorous definition of "pathological input"?
>>>>>>>>>>
>>>>>>>>>> Is there an algorithm to determine whether a given input is
>>>>>>>>>> "pathological" or not?
>>>>>>>>>>
>>>>>>>>>> I could define an is_prime() function like this:
>>>>>>>>>>
>>>>>>>>>>        bool is_prime(int n) {
>>>>>>>>>>            return n >= 3 && n % 2 == 1;
>>>>>>>>>>            // returns true for odd numbers >= 3, false for
>>>>>>>>>>            all others
>>>>>>>>>>        }
>>>>>>>>>>
>>>>>>>>>> I'll just say that odd numbers that are not prime are 
>>>>>>>>>> pathological
>>>>>>>>>> input, so I don't have to deal with them.
>>>>>>>>>
>>>>>>>>> Pathological input:
>>>>>>>>>
>>>>>>>>> Self-referencial to the decider.
>>>>>>>>
>>>>>>>> OK.
>>>>>>>>
>>>>>>>> Do you have a *rigorous* definition of "pathological input"?
>>>>>>>>
>>>>>>>> Is there an algorithm to determine whether a given input is
>>>>>>>> "pathological" or not?
>> [...]
>>>>>> Examples are not definitions.
>>>>>>
>>>>>> And the problem is that the above example is itself a category error
>>>>>> for the problem, as the DD provided above isn't a complete 
>>>>>> program, as
>>>>>> it doesn't include the code for HHH as required, and when you include
>>>>>> Halt7.c as part of the input, your HHH isn't a seperate program of 
>>>>>> its
>>>>>> own, and thus doesn't have a Turing Complete range of inputs it can
>>>>>> accept.
>>>>>>
>>>>>> Sorry, you are just showing you don't understand what it means to
>>>>>> DEFINE something.
>>>>>
>>>>> Ah, the fundamental mistake you have been making all this time, Damon!
>>>>> The self-referencial category error doesn't magically disappear by
>>>>> providing source code rather than a run-time function address to the
>>>>> decider; you are simply transforming the same input without affecting
>>>>> the result.
>>>>>
>>>>> /Flibble
>>>>
>>>> And WHAT is the category error?  You stil can't show the difference in
>>>> CATEGORY between what is allowed and what isn't, and in fact, you can't
>>>> even precisely define what is and isn't allowed.
>>>>
>>>> Now, you also run into the issue that the "Olcott System" begins 
>>>> with an
>>>> actual category error as we do not have the required two seperate
>>>> programs of the "Decider" and the "Program to be decided on" given via
>>>> representation as the input, as what you want to call that program 
>>>> to be
>>>> decided isn't one without including the code of the decider it is 
>>>> using,
>>>> and when you do include it, the arguments about no version of the
>>>> decider being able to succeed is improper as it must always be that
>>>> exact program that we started with, and thus it just FAILS to do a
>>>> correct simulation, while a correct simulation of this exact input
>>>> (which includes the ORIGINAL decider) will halt.
>>>>
>>>> Sorry, YOU are the one stuck with the fundamental mistake, or is it a
>>>> funny mental mistake because you don't understand what you are talking
>>>> about.
>>>
>>> The category error is extant over the domain of pathological inputs, no
>>> matter what form those inputs take.
>>
>> That certain is a lot of words.
>>
>> Do you have a rigorous definition of "pathological input"?
>>
>> Is there an algorithm to determine whether a given input is
>> "pathological" or not?
>>
>> "Yes" and "No" could be valid answers to either of those questions.
>> Nothing you have written above is an answer to either of those
>> questions.
>>
>> Are you able to answer those questions?
>>
> 
> Objective and Subjective Specifications
> Eric C.R. Hehner
> Department of Computer Science, University of Toronto
> 
> (6) Can Carol correctly answer “no” to this (yes/no) question?
> https://www.cs.toronto.edu/~hehner/OSS.pdf
> 
> Pathological inputs are such that
> Does the input halt on its input?
> Both yes and no are the wrong answer.
> 
> Carol's question is an example of this.
> 
> Richard Damon found a loophole in the original question.
> I inserted (yes/no) to close the loophole.
> 

And the problem you run into is that the actual Halting Question is 
Objective, what is the behavior of the machine described by the input, 
but you try to change it, by breaking the computation system, into the 
subjective question of what can H return to be correct.

Sorry, your logic is just based on lies and errors.